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This paper addresses the data-driven identification of latent representations of partially observed dynamical systems, i.e., dynamical systems for which some components are never observed, with an emphasis on forecasting applications and long-term asymptotic patterns. Whereas state-of-the-art data-driven approaches rely in general on delay embeddings and linear decompositions of the underlying operators, we introduce a framework based on the data-driven identification of an augmented state-space model using a neural-network-based representation. For a given training dataset, it amounts to jointly reconstructing the latent states and learning an ordinary differential equation representation in this space. Through numerical experiments, we demonstrate the relevance of the proposed framework with respect to state-of-the-art approaches in terms of short-term forecasting errors and long-term behavior. We further discuss how the proposed framework relates to the Koopman operator theory and Takens' embedding theorem., This work was supported by Labex Cominlabs (grant SEACS), Region Bretagne, CNES (grant OSTST-MANATEE), and Microsoft (AI EU Ocean awards) and by MESR, FEDER, Région Bretagne, Conseil Général du Finistère, Brest Métropole, and Institut Mines Télécom in the framework of the VIGISAT program managed by “Groupement Bretagne Télédétection,” CNES (grant OSTST-MANATEE), and ANR (Melody and OceaniX grants). It benefited from HPC and GPU resources from Azure (Microsoft EU Ocean awards) and from GENCI-IDRIS (Grant No. 2020-101030).

16 pages, 12 figures, 2 tables, Knowledge of ocean surface current at high resolutions is crucial for many applications. In addition to the classic satellite altimetry retrieval from sea surface height (SSH), ocean surface currents can be retrieved from sea surface temperature (SST) observations using a transfer function between SST and SSH. Previous works showed the potential of microwave SST observations to reconstruct ocean surface currents using a synergistic approach: an optimal transfer function that combines the phase of SST with the SSH amplitude spectra. This synergistic approach revealed that surface quasi geostrophy (SQG) reconstruction can be enhanced and opened up the possibility to improve spatial resolution of ocean currents retrieved from altimeters observations if infrared SST observations are considered. However, before applying this synergistic approach to satellite observations, we need to analyze and characterize the spectral properties of the transfer function. This spectral characterization of the transfer function allows to exploit the synergy between SST and SSH observations that have different measurement topology and different spatial resolution. Here, we performed a feasibility study using the daily outputs of the operational Mercator global analysis and forecast system at (1/12)° in the western coast of Australia (27–35°S, 107–113°E) spanning from 26 November 2012 to 26 November 2016. Results showed that the mean transfer function in this region presents two well different bands: one characterized by a negative slope slightly steeper (α = −1.2) than the k−1 predicted by the SQG solution for scales smaller than 270 km and another characterized by a plateau for wavelengths larger than 270 km. In addition, the results revealed that the inhomogeneity in dynamics of the flow limits global solutions. Finally, we showed that information contained along the track is enough for a synoptic reconstruction of the flow in this region, which shows the feasibility of applying this methodology to real satellite observations, This work was mainly supported by the ESA Scientific Exploitation of Operational Missions (SEOM) Living Planet Fellowship OCEANUS. This work was also partially supported by public funds (Ministère de l'Education Nationale, de l'Enseignement Supérieur et de la Recherche, FEDER, Région Bretagne, Conseil Général du Finistère, Brest Métropole) and by Institut Mines Télécom, received in the framework of the VIGISAT project managed by “Groupement Bretagne Télédétection” (BreTel). J. I. F. acknowledges the support by the European Space Agency through the GlobCurrent Data User Element project (4000109513/13/I‐LG), by the Convocatoria Programa Estatal de I+D+i Orientada a los Retos de la Sociedad del año 2016 in the framework of COSMO project (CTM2016‐79474‐R) and from Fundación General CSIC (Programa ComFuturo). This study has been conducted using E.U. Copernicus Marine Service Information (Product identifier: GLOBAL_ANALYSIS_FORECAST_PHY_001_024), With the funding support of the ‘Severo Ochoa Centre of Excellence’ accreditation (CEX2019-000928-S), of the Spanish Research Agency (AEI)

The Iron Age stelae from Cornouaille (Finistère, France) display a great variety of shapes and lithological types. They are monolithic monuments, partly or entirely carved. Their morphology can result from the natural shaping of rock blocks or they may have an architectural form. In the latter case, the stelae are built around an axis. Their volume can be decomposed into three parts : top, shaft and baseplate. The shaft sides may be decorated. In the context of the inventory initiated by the Centre de l’archéologie du Conseil départemental du Finistère, the purpose of this study is to highlight the specific contributions of both petrography and rock structural analysis to the identification of extraction sites of the Cornouaille stelae, as well as to the understanding of shaping and transportation modes. The methodology is based on the comparative study, on macro-and microscopic scales, of both the monuments and the surrounding geological massifs. The latter are parts of the Variscan crystalline basement of Armorica which recorded strain, metamorphism and granitisation about 300 million years ago. Four criteria have been taken into account : 1) comparative analysis of the natural forms (as either erosional features or tectonic fabric) of the rock blocks in the inferred source massifs and the general shapes of the monuments assumed to have been extracted from them ; 2) texture of the rocks (grain size and crystal relations) ; 3) structure of the rocks (isotropic or strained — schistosity plane and lineation — presence of Z-or S-shaped stretched megacryst) ; and 4) mineralogy. Two test-zones have been selected : the Cap Sizun and Concarneau areas. Stela density is very high in the first area, where fifty-six uniformly distributed monoliths were identified. No stela has been found in an archaeological context. In the Concarneau area, with a nearly equal surface, only twenty-eight stelae are recorded. The archaeological context of two of them, adorned with fluting, is well-known. A first result is that the stela location is generally either within or near the boundaries of the massifs having a similar granitic or meta morphic lithology. The Cap Sizun stelae are characterized by a greater petrographic homogeneity than in the other area, up to more than four kilometres from the boundary of the source granitic massif. Another original result has been the demonstration that the Iron Age artisans used natural forms and that the latter result from two contrasted mechanisms : 1) various erosional processes for the small granitic stelae and 2) high tectonic strain for the tall cigar-shaped gneissic stelae. It would thus seem that the Iron Age artisans usually used pre-existing natural morphologies of stones with a view to shaping their monoliths with the least possible effort or for reasons of symbolism. Regarding the four specific stelae in Nizon orthogneiss (Concarneau area), two potential extraction zones have been identified fairly precisely, by mapping various types of highly strained orthogneisses, referred to as ‘ tectonites’ : S/ L-tectonites, dominated by both flattening and stretching (corresponding exactly to one of the gneissic stelae), and L-tectonites that no longer display any flattening plane, but instead a prominent stretching lineation (corresponding to the other three gneissic stelae). One of the two potential extraction sites (Moulin du Chef-du-Bois, La Forêt Fouesnant) includes natural cylinders with 3D-dimensions quite comparable to those of the gneissic stelae. Furthermore, the presence of an unfinished stela to the north of Cap Sizun, a few kilometres away from the northern limit of the source massif, indicates than this monument was probably shaped close to the final erection site rather than near its extraction zone. Thus, it would appear that the Cap Sizun artisans moved rough granitic blocks rather than shaped stelae. Finally, the location of two granitic stelae in the Concarneau area near a ria, away from the assumed granitic massif source, suggests that they were moved using maritime transport for a distance of about six kilometres., Les stèles de l’âge du Fer de Cornouaille (Finistère) montrent une très grande variété de formes et de lithologies. Dans le cadre de l’inventaire initié par le centre départemental de l’Archéologie du conseil départemental du Finistère, l’objectif de cette étude est de préciser les contraintes que peuvent apporter la pétrographie et l’analyse structurale des roches sur l’identification des sites d’extraction des stèles de Cornouaille, ainsi que sur la compréhension des modalités de façonnage et de transport. La méthodologie est basée sur l’étude comparative, macro-et microscopique, des monuments et des principaux massifs géologiques des secteurs géographiques considérés. Ces massifs appartiennent au vieux socle hercynien armoricain, structuré vers 300 millions d’années, et constitué, dans la zone d’étude, par des roches granitiques et métamorphiques. Deux zones tests ont été sélectionnées : les secteurs du cap Sizun et de Concarneau. Notre premier résultat est de montrer que les stèles sont en général localisées dans les limites des massifs de lithologie correspondante ou à quelques kilomètres de leur bordure. Les stèles du cap Sizun se caractérisent par une plus grande homogénéité lithologique que celles de l’autre secteur, et ce jusqu’à une distance qui peut excéder de quatre kilomètres la limite du massif source (granite de la pointe du Raz). Un autre résultat original est la mise en évidence de l’utilisation de formes naturelles par les artisans de l’âge du Fer : diverses morphologies d’érosion pour les petites stèles granitiques des deux secteurs et un débit tectonique «en cigare » pour les stèles hautes gneissiques. Pour le cas très particulier des quatre monuments en gneiss de Nizon du secteur de Concarneau, deux zones d’extraction potentielles ont pu être identifiées avec une bonne précision. Concernant les modalités de transport des monuments, la présence d’une stèle inachevée au nord du cap Sizun, à plusieurs kilomètres de la bordure septentrionale du massif granitique source, indique que ce monolithe n’a vraisemblablement pas été façonné sur son lieu d’extraction, avant transport, mais plutôt près de son lieu d’érection. Il semblerait donc que les artisans du cap Sizun aient pu déplacer les blocs granitiques bruts ou simplement ébauchés plutôt que les monuments finis. Enfin, notre étude permet d’avancer l’hypothèse que deux stèles granitiques du secteur de Concarneau ont été transportées par voie maritime., Caroff Martial, Grall Bertrand, Moysan Marine, Le Gall Bernard, Cherel Anne-Françoise. Aires d’extraction et façonnage des stèles de l’âge du Fer de Cornouaille (Finistère, France) : apports de la pétrographie et de l’analyse structurale des roches. In: Bulletin de la Société préhistorique française, tome 113, n°4, 2016. pp. 765-784.